Membrane Scattering with M-Momentum Transfer
Joseph Polchinski, Philippe Pouliot
TL;DR
The paper addresses whether matrix theory correctly captures 11-dimensional Lorentz invariance by computing membrane scattering with one unit of $M$-momentum transfer. It maps the process to a three-dimensional $SU(2)$ instanton problem and derives the matrix-theory amplitude, showing it matches the corresponding eleven-dimensional supergravity result in a regime of large $b$ and strong coupling, with an explicit velocity-dependent integrand $\frac{1}{16 R_{11}^3 M_{11}^3} \int d^3x' \frac{(\dot X_\perp^2)^2}{X^3} e^{-(X/\gamma - i X^{11})/R_{11}}$. This agreement provides a nontrivial check of 11D Lorentz invariance within matrix theory and illustrates how nonperturbative instanton effects encode M-theory dynamics, while highlighting the role of supersymmetry in constraining but not fully fixing the normalization and pointing to directions for extending the tests to less-supersymmetric regimes and other scattering channels.
Abstract
Membrane scattering in m(atrix) theory is related to dynamics in three-dimensional $SU(2)$ gauge theory, with transfer of $p^{11}$ being an instanton process. We calculate the instanton amplitude and find precise agreement with the amplitude in eleven dimensional supergravity.